Heralded Quantum Gate between Remote Quantum Memories

We demonstrate a probabilistic entangling quantum gate between two distant trapped ytterbium ions. The gate is implemented between the hyperfine “clock” state atomic qubits and mediated by the interference of two emitted photons carrying frequency encoded qubits. Heralded by the coincidence detection of these two photons, the gate has an average output state fidelity of $89\pm 2\%$. This entangling gate together with single qubit operations is sufficient to generate large entangled cluster states for scalable quantum computing.

Figure 1

The experimental apparatus. Two ${}^{171}\mathrm{Yb}^{+}$ ions are trapped in identically constructed ion traps separated by 1 m. A magnetic field $\mathsf{B}$ is applied perpendicular to the excitation and observation axes to define the quantization axis. About 2% of the emitted light from each ion is collected by an imaging system (OL) with numerical aperture of about 0.3 and coupled into single-mode fibers. Polarization control paddles are used to adjust the fibers to maintain linear polarization. The output of these fibers is directed to interfere on a polarization-independent 50% beam splitter (BS). Polarizers (PBS) transmit only the $\pi$-polarized light from the ions. The photons are detected by single-photon counting photomultiplier tubes (PMT A and PMT B). Detection of the atomic state is done independently for the two traps with dedicated photomultiplier tubes (PMTs).

Figure 2

(a) Level and excitation scheme. The qubit is encoded in the ${}^{2}S_{1/2}$ hyperfine clock states of the ${}^{171}\mathrm{Yb}^{+}$ ion and is coherently excited to the ${}^{2}P_{1/2}$ hyperfine excited states by a pulse from an ultrafast laser with a wavelength centered near 369.5 nm. Upon spontaneous emission of a $\pi$-polarized photon, the frequency state of the photon is entangled with the qubit state of the atom. A polarizer (PBS) blocks photons from different decay channels. (b) Gate operation scheme. After initialization in $|0⟩$, ion 1 and 2 are prepared in the input states $|{\Psi }_a{⟩}_1$ and $|{\Psi }_a{⟩}_2$, respectively. The frequency of each spontaneously emitted $\pi$-polarized photon is entangled with the state of the respective ion. If these two photons are detected in the antisymmetric Bell state, the quantum state of the two ions is projected on the state $|{\Psi }_{aa}⟩\propto Z_1(I-Z_1{Z}_2)|{\Psi }_a{⟩}_1|{\Psi }_a{⟩}_2$. Here $Z_i$ is the Pauli-$z$ operator acting on ion $i$.

Figure 3

State Tomography of the final state $|{\Psi }_{aa}⟩\propto Z_1(I-Z_1{Z}_2)(|0+1{⟩}_1|0+1{⟩}_2)$. Real (a) and imaginary (b) part of the reconstructed density matrix. The fidelity of the expected output state $|0{⟩}_1|1{⟩}_2-|1{⟩}_1|0{⟩}_2$ of the gate is $F=0.87(2)$. The generated state has a concurrence of $C=0.77(4)$ and an entanglement of formation of $E_F=0.69(6)$. The density matrix is obtained with a maximum likelihood algorithm from 601 events measured in 9 different bases.